Free Printable GPPPU1-8 SY2026 (Poly, Proofs, Cong, Sim, RightTri, Vol, Prob)

1.

PRIORITY PRACTICE PROBLEMS (u1: Poly)

[BEGIN U1: Exploring Polynomial Expressions Through Geometry]

These problems are grouped in sets of 4 in this order ... 1. Add / Subtract Polynomials 2. Multiply Polynomials 3. Perimeter of <?> 4. Area of <?>

What is PERIMETER?

4 lines

2.

Simplify this expression:
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

3.

Simplify this expression:
(r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

4.

Find the perimeter of the triangle ...

a)

$4x+64$

b)

$4x^2+64$

c)

$3x+50$

d)

$3x^2+50$

5.

The following image is a square. Find the PERIMETER AND AREA of the square.

a)

PERIMETER: $16x^3$ AREA: $16x^6$

b)

PERIMETER: $16x^6$ AREA: $16x^3$

c)

PERIMETER: $8x^3$ AREA: $8x^6$

d)

PERIMETER: $8x^6$ AREA: $8x^3$

6.

Simplify this expression:
(2a² + 5a + 3) - (a² - 3a - 4)

a)

3a² + 2a - 1

b)

a²+ 8a + 7

c)

3a²+ 8a + 7

d)

a² + 2a - 1

7.

Simplify this expression:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

8.

Find the perimeter of the rectangle ...

a)

P= 10x + 2

b)

P= 12x

c)

P = 12

d)

P = 6x² + 3x

9.

Find the area of the rectangle ...

a)

A= 10x + 2

b)

A= 6x² + 3x

c)

A= 9x

d)

A= 6x+ 3

10.

Simplify this expression:

(x² + 5x - 4) - (- x² + 4x + 6)

a)

2x² + x + 2

b)

x + 2

c)

2x² + x - 10

d)

x - 10

11.

Simplify this expression:
(3x² – 1)(x² + 5)

a)

17x² -5

b)

3x⁴ + 7x² - 5

c)

3x⁴ + 14x² - 5

d)

3x⁴ + 14x² + 5

12.

a)

6b

b)

b + 5

c)

b + 9

d)

b - 13

13.

Find the area of the rectangle ...

a)

$42x^3+28x^2$

b)

$42x^2+28x^{ }$

c)

$42x^3+4x^2$

d)

$13x^3+11x^2$

14.

Simplify this expression:
(3x² + 4x – 1)(x² + 5)

a)

3x⁴ + 4x³ + 14x² + 20x − 5

b)

3x⁴ + 4x³ + 14x² + 20x + 5

c)

3x⁴ + 4x³ - x²- 5

d)

15x² + 20x - 5

15.

Simplify this expression:
(4a² + 5a + 4) - (2a² - 8a - 4)

a)

6a²- 3a + 8

b)

2a²+ 13a

c)

2a²+ 13a + 8

d)

6a²- 3a

16.

a)

4x

b)

4x + 30

c)

4x - 30

d)

4x + 2

17.

Find the area of the rectangle ...

a)

$18x^2-48x+6$

b)

$18x^3-48x+6x$

c)

$18x^3-48x^2+6x$

d)

$9x^3-14x^2+7x$

18.

Simplify this expression:

(2x² + 6x - 3) - (- 2x² - 4x + 6)

a)

4x² + 10x + 9

b)

10x + 9

c)

10x - 9

d)

4x² + 10x − 9

19.

Simplify this expression:
(3x² + 4x – 1)(3x² + 5)

a)

9x⁴ + 12x³ + 12x² + 20x + 5

b)

3x⁴ + 4x³ + 14x² + 20x + 5

c)

3x⁴ + 4x³ - x²- 5

d)

9x⁴ + 12x³ + 12x² + 20x − 5

20.

What is the perimeter of the rectangle?

a)

24w³ – 4

b)

24w⁵ – 4

c)

17w² + 3w³

d)

32w³ + 16w² – 8

21.

Find the perimeter ...

a)

7x + 5

b)

24x + 4

c)

9x + 5

d)

9x² + 5

22.

The dimensions of a rectangle are (4y² – y + 6) feet by (2y² + 3) feet. What is the perimeter of the rectangle?

a)

12y² – 2y + 18 feet

b)

6y² – y + 9 feet

c)

2y² – 2y + 3 feet

d)

12y² – y + 9 feet

23.

^{The perimeter of the triangle is 10x+20.}

^{Find the length of the missing side (marked with '?') ...}

a)

6x+10

b)

15x+30

c)

5x+10

d)

5x-10

24.

What is the area of the rectangle?

a)

24w³ – 4

b)

56x⁶ + 56x⁵ − 32x³ − 32x²

c)

56x⁶ + 56x⁵ − 32x³ + 32x²

d)

32w³ + 16w² – 8

25.

Find a simplified expression for the area of the shaded region.

a)

2x²+ 2x + 13

b)

10x + 5

c)

10x + 13

d)

2x²+ 13

26.

PRIORITY PRACTICE PROBLEMS (u2: Proofs) (Problems 26 - 110)

U2 (Geometric Foundations and Proofs) ... these "Priority Practice Problems" are organized in the following order ...

Vocabulary and Language (5 problems) (26-30)
Angle and Segment Addition (7 problems) (31-37)

Triangle Sum Theorem | Exterior Angles Theorem (13 problems) (38-50)

Parallel Lines (15 problems) (51-65)

Parallel Line Proofs (20 problems) (66-85)

Quadrilateral Properties (10 problems) (86-95)

(Coordinate) Quadrilateral Proofs (15 problems) (96-110)

[BEGIN VOCABULARY and LANGUAGE] ∠1 and ∠3 can best be described as ...

a)

complementary angles

b)

supplementary angles

c)

vertical angles

d)

adjacent angles

27.

In angle ABC, B is the ...

a)

rays

b)

plane

c)

compass

d)

vertex

28.

In angle ABC, BA and BC are ...

a)

rays

b)

plane

c)

compass

d)

vertex

29.

What does this symbol mean?

a)

less than

b)

greater than

c)

congruent

d)

similar

30.

[END VOCABULARY and LANGUAGE] Name that figure!

a)

Point

b)

Line

c)

Line segment

d)

Ray

31.

[BEGIN Angle and Segment Addition] Find the missing segment length / encontrar la longitud del segmento que falta ...

a)

24

b)

6

c)

9

d)

15

32.

Use the figure to write and solve an equation for x.

a)

5

b)

6

c)

7

d)

8

33.

a)

8

b)

12

c)

-4

d)

-8

34.

B is the midpoint of AC. Find AB.

a)

2

b)

16

c)

8

d)

4

35.

Find the value of ∠A.

a)

25 degrees

b)

30 degrees

c)

35 degrees

d)

90 degrees

36.

Calculate m∠ABC.

a)

45°

b)

60°

c)

105°

d)

15°

37.

[END Angle and Segment Addition] If m∠ABC = 103° find x.

(a)

38.

[BEGIN Triangle Sum Theorem] The Triangle Sum Theorem: The sum of the 3 angles in a triangle is ______.

a)

45°

b)

90°

c)

180°

d)

360°

39.

Find the measure of the indicated angle.

a)

$135\degree$

b)

$55\degree$

c)

$45\degree$

d)

$60\degree$

40.

Find the measure of the indicated angle.

a)

$45\degree$

b)

$33\degree$

c)

$123\degree$

d)

$147\degree$

41.

[END Triangle Sum Theorem] Solve for x.

a)

16

b)

11

c)

50

d)

6

42.

[BEGIN Exterior Angle Theorem] Which of the following terms best describes Angle d?

a)

Remote interior angle

b)

Corresponding angle

c)

Exterior angle

d)

Interior angle

43.

Which of the following angles are remote interior angles to angle d?

a)

Angle a and Angle b

b)

Angle b and Angle c

c)

Angle a and Angle c

d)

Angle a and Angle b and Angle c

44.

Which two angles are the remote interior angles to Angle W?

a)

Angle X and Angle Y

b)

Angle X and Angle Z

c)

Angle Y and Angle Z

d)

Angle Z and Angle W

45.

Solve for the missing angle with the question mark.

a)

A

b)

B

c)

C

d)

D

46.

What is the value of the missing angle?

a)

90

b)

100

c)

20

d)

120

47.

What is the value of x?

a)

105°

b)

144°

c)

69°

d)

111°

48.

a)

A

b)

B

c)

C

d)

D

49.

Find the indicated angle measure. (What is ?)

a)

51°

b)

37°

c)

167°

d)

41°

50.

[END Exterior Angle Theorem] What is the value of x?

a)

38

b)

57

c)

76

d)

85

51.

[BEGIN Parallel Lines and Transversals] What word describes line Z?

a)

Transversal

b)

Corresponding

c)

Consecutive Interiors

52.

What angle corresponds to angle 6?

a)

angle 2

b)

angle 4

c)

angle 7

d)

angle 8

53.

Name the angle relationship.

a)

Alternate Interior

b)

Alternate Exterior

c)

Corresponding

d)

Vertical Angles

54.

Name the angle relationship.

a)

Consecutive Interior

b)

Corresponding

c)

Alternate Interiors

d)

Alternate Exteriors

55.

Name the angle relationship.

a)

Alternate Interior

b)

Alternate Exterior

c)

Corresponding

d)

Vertical Angles

56.

If angle 6 is 25 degrees, how many degrees is angle 7?

a)

25 degrees

b)

50 degrees

c)

90 degrees

d)

155 degrees

57.

If the m∡1 = 118^o find m∡5

a)

118^o

b)

62^o

c)

82^o

d)

2^o

58.

If the m∡7 = 62^o find m∡1

a)

62^o

b)

28^o

c)

118^o

d)

138^o

59.

If the m∡3 = 81^o find m∡6

a)

180^o

b)

99⁰

c)

9^o

d)

81^o

60.

If the m∡2 = 32^o find m∡3

a)

132^o

b)

32^o

c)

148^o

d)

58^o

61.

If the m∡5 = 125^o find m∡1

a)

125^o

b)

35^o

c)

55^o

d)

100^o

62.

If the m∡6 = 71^o find m∡3

a)

171^o

b)

19^o

c)

109^o

d)

71^o

63.

If the m∡3 = 35^o find m∡8

a)

35^o

b)

55⁰

c)

135^o

d)

145^o

64.

If the m∡7 = 60^o find m∡2

a)

7^o

b)

60^o

c)

30⁰

d)

120^o

65.

[END Parallel Lines and Transversals] Solve for y.

a)

$y=55$

b)

$y=35$

c)

$y=70$

d)

$y=45$

66.

[BEGIN Parallel Lines Proofs] If A=B and B=C, then A=C. What is this property?

a)

Transitive

b)

Reflexive

c)

Symmetric

d)

Substitution

67.

If a = b, then a may be replaced by b in any expression.

a)

Transitive Property

b)

Reflexive Property

c)

Symmetric Property

d)

Substitution Property

68.

Analogy

Transitive is to Congruence, as Substitution is to ???

a)

Equalities

b)

Congruences

c)

Both

d)

None of the above

e)

I don't Know

69.

For any number a, a = a.

a)

Transitive Property

b)

Reflexive Property

c)

Symmetric Property

d)

Substitution Property

70.

If you know that angles 1 and 2 are vertical, what else do you know?

a)

Angles 1 and 2 are congruent

b)

Angles 1 and 2 are supplementary

c)

Angles 1 and 2 are right angles

d)

Angles 1 and 2 are corresponding angles

71.

If A=10, then wherever there is an "A" value, you could replace it with 10. What property is this?

a)

Substituion

b)

Transitive

c)

Symmetric

d)

Plug it in

72.

When two parallel lines are cut by a transversal, all pairs of angles created are either _________ or _________.

a)

Congruent, supplementary

b)

Congruent, complementary

c)

Supplementary, complementary

d)

Corresponding, vertical

73.

What is the relationship of ∠1 and ∠5?

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

Vertical Angles

74.

What is the relationship of ∠4 and ∠7?

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

Linear Pair

75.

What is the relationship of ∠3 and ∠4?

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

Linear Pair

76.

What is the relationship of ∠6 and ∠8?

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

Linear Pair

77.

What statement can be made from the diagram using the Corresponding Angles Postulate?

a)

∠1 and ∠2 are supplementary

b)

m∠1 + m∠2 = 180°

c)

∠1 ≅ ∠2

d)

m∠1 = m∠2

78.

What statement can be made from the diagram using the Alternate Interior Angles Theorem?

a)

∠1 and ∠2 are supplementary

b)

m∠1 + m∠2 = 180°

c)

∠1 ≅ ∠2

d)

m∠1 = m∠2

79.

What statement can be made from the diagram using the Alternate Exterior Angles Theorem?

a)

∠1 and ∠2 are supplementary

b)

m∠1 + m∠2 = 180°

c)

∠1 ≅ ∠2

d)

m∠1 = m∠2

80.

What statement can be made from the diagram using the Consecutive Interior Angles Theorem?

a)

∠1 and ∠2 are supplementary

b)

m∠1 + m∠2 = 180°

c)

∠1 ≅ ∠2

d)

m∠1 = m∠2

81.

Supply the first statement.

a)

m ll n

b)

< 4 = < 6

c)

Given

d)

Definition of parallel lines

82.

Supply the second reason.

a)

Linear Pair Postulate

b)

Alternate Interior Angles Theorem

c)

Vertical Angles Theorem

d)

Corresponding Angles Postulate

83.

Supply the third reason.

a)

Vertical Angle Theorem

b)

Corresponding Angles Postulate

c)

Alternate Interior Angles Postulate

d)

Same Side Interior Angles Theorem

84.

The last statement is <4 = <6. What is the last reason

a)

Prove

b)

Definition of congruent angles

c)

Transitive Property

d)

Alternate Interior Angles Theorem

85.

[END Parallel Lines Proofs] Which proof is incorrect?

a)

b)

c)

d)

86.

[BEGIN Quadrilateral Properties] What is the most specific name for this shape?

a)

Square

b)

Rectangle

c)

Rhombus

d)

Parallelogram

87.

What shape is this?

a)

Kite

b)

Square

c)

Trapezoid

d)

Rhombus

88.

What shape is this?

a)

Square

b)

Parallelogram

c)

Trapezoid

d)

Rhombus

89.

This is a parallelogram. What is the value of x?

a)

7

b)

12

c)

112

d)

68

90.

This is a parallelogram. What is the value of y?

a)

7

b)

12

c)

112

d)

68

91.

This is a parallelogram. What is the value of a?

a)

7

b)

12

c)

112

d)

68

92.

Select the most specific name for each of the following quadrilaterals shown to the left

a)

Parallelogram

b)

Rhombus

c)

Trapezoid

d)

Square

e)

Rectangle

93.

Select the most specific name for each of the following quadrilaterals shown to the left

a)

Parallelogram

b)

Rhombus

c)

Trapezoid

d)

Square

e)

Rectangle

94.

Find the missing angle.

a)

30

b)

60

c)

90

d)

120

95.

[END Quadrilateral Properties] Find the measure of the angle x.

a)

105

b)

115

c)

65

d)

75

96.

[BEGIN (Coordinate) Quadrilateral Proofs] What is this formula used for?

$\frac{y_2-y_1}{x_2-x_1}$

a)

To find the distance between two points

b)

To find the slope between two points

c)

To find the midpoint between two points

97.

What is the formula below used for?

\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

a)

To find the distance between two points

b)

To find the slope between two points

c)

To find the midpoint between two points

98.

Josie found the slope of AB to be

\frac{3}{4}

. Use rise over run to check her answer.

a)

No, the slope should be $\frac{4}{3}$

b)

She was correct.

99.

Brad proved that ABCD is a parallelogram by proving both sets of opposite sides to be parallel. What should he do next if he wants to prove it is a rhombus?

a)

Find the distance of each line to see if they are congruent.

b)

Compare the slopes of adjacent sides to see if they are perpendicular.

100.

Brad proved that ABCD is a parallelogram and that all sides had the same distance What should he do next if he wants to prove it is a square?

a)

He doesn't need to do anything else, it looks like a square so he is all set.

b)

Compare the slopes of adjacent sides to see if they are perpendicular.

101.

In the image, side AB has a slope of -3 and AD has a slope of 1/3. What does this mean is true?

a)

Side AB and AD are parallel

b)

Side AB and AD form a right angle

c)

Side AB and AD are congruent

d)

Nothing Specific

102.

Drew used the distance formula and found each side to have a distance of 4. What does that mean?

a)

Side AB and AD are parallel

b)

Side AB and AD form a right angle

c)

Side AB and AD are congruent

d)

Nothing Specific

103.

The slope of side AB is -3 and the slope of DC is -3. What does this mean?

a)

Side AB and AD are parallel

b)

Side AB and AD form a right angle

c)

Side AB and AD are congruent

d)

Nothing Specific

104.

Julia proved ABCD is a parallelogram. She notices that side AB has a slope of 8/3 and BC has a slope of 1/3. What can she classify ABCD as?

a)

A rectangle

b)

A square

c)

A rhombus

d)

Just a parallelogram

105.

Use the distance formula to see if side AB is congruent to side BC.

a)

Yes they are congruent

b)

No, they are not congruent

106.

Use the distance formula to see if side BC is congruent to side AD.

a)

Yes they are congruent

b)

No, they are not congruent

107.

What is the most specific name for quadrilateral ARMY?

a)

Paralellogram

b)

Square

c)

Rectangle

d)

Rhombus

108.

What is the most specific name for quadrilateral DOGS?

a)

Rhombus

b)

Rectangle

c)

Parallelogram

d)

Square

109.

What is the most specific name for quadrilateral FISH?

a)

Parallelogram

b)

Square

c)

Rectangle

d)

Rhombus

110.

[END (Coordinate) Quadrilateral Proofs] What is the most specific name for quadrilateral NOSE?

a)

Square

b)

Parallelogram

c)

Rectangle

d)

Rhombus

111.

[RESUME U3: Exploring Congruence (SEE Q1-Q10)] What does SAS stand for?

a)

Side-Angle-Side

b)

Super-Awesome-Side

c)

Side-Angle-Supersized

d)

Sensationally Awesome Superman

112.

Which is NOT a test to prove triangles congruent?

a)

SAA

b)

SSS

c)

SSA

d)

SAS

113.

What are the five ways to prove triangles congruent?

a)

SSS, ASA, AAS, SAS, HL

b)

SSS, SSA, HL, AAS, SAS

c)

SAS, SSA, HL, AAS, SSS

d)

HL, SAS, SSA, SSS, ASA

114.

Complete the congruence statement.

a)

CRP

b)

PCR

c)

RPC

d)

PRC

115.

Use the congruency statement to answer the following:
<F = ___

a)

<H

b)

<I

c)

<G

d)

not congruent to another angle

116.

Are these triangles congruent? If so, state the rule which you used to determine congruence.

a)

Yes by ASA

b)

Yes by AAS

c)

Yes by SSA

d)

Not congruent

117.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

AAS

118.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

AAS

119.

Are these triangles congruent?

a)

Yes, by AAS

b)

Yes, by SAS

c)

Yes, by SSS

d)

No, this is the SSA one!!

120.

What is always the 1st statement in reason column of a proof?

a)

Prove

b)

Given

c)

Reason

d)

Statement

121.

Fill in the blank.

a)

Given

b)

Reflexive Property

c)

Transitive Property

d)

They're the same side!!!!!!

122.

What additional information is required to prove the 2 triangles are congruent by ASA

a)

A)

b)

B)

c)

C)

d)

D)

123.

Which of the following are NOT sufficient to prove two triangles are congruent? Choose all that apply.

a)

SSS

b)

AAA

c)

ASA

d)

SSA

e)

AAS

124.

Are these triangles congruent?

a)

Yes, by SSS

b)

Yes, by SAS

c)

Yes, by AAS

d)

Yes, by HL

125.

Identify the missing statement or reason

a)

Reflexive Property

b)

Definition of Midpoint

c)

Given

d)

Vertical Angles Theorem

126.

Identify the missing statement or reason

a)

Definition of Angle Bisector

b)

Alternate Interior Angles Theorem

c)

Reflexive Property

d)

Definition of Midpoint

127.

a)

A

b)

B

c)

C

d)

D

128.

a)

A

b)

B

c)

C

d)

D

129.

Which statement is true for

\Delta ABC\cong\Delta DEF

a)

$\angle A\cong\angle B$

b)

$\angle A\cong\angle F$

c)

$\angle A\cong\angle D$

d)

$\angle A\cong\angle E$

130.

[END U3: Exploring Congruence (SEE Q1-Q10)] Which statement is true for

$\Delta ABC\cong\Delta DEF$

a)

$\overline{BC}\cong\overline{DE}$

b)

$\overline{BC}\cong\overline{EF}$

c)

$\overline{BC}\cong\overline{DF}$

131.

[BEGIN U4 Investigating Similarity Test Review U4TR][LANGUAGE] What word was used a lot in this unit?

2 lines

132.

[LANGUAGE] Which of the following is NOT a rigid transformation?

a)

dilation

b)

translation

c)

rotation

d)

reflection

133.

[LANGUAGE] Which statement describes a dilation?

a)

ALWAYS makes a figure larger

b)

preserves side lengths and angles

c)

changes angles and side lengths

d)

preserves angles, but changes side lengths

134.

[LANGUAGE] What statement(s) best describe the difference between similar and congruent?

a)

They are the same!

b)

Similar means "alike in some ways", and congruent means "exactly the same"

c)

Similar is harder to pronounce, and congruent is harder to spell

d)

The similar operator is ~ ... the congruent operator is ≅

135.

[LANGUAGE] A dilation's scale factor is used to perform what arithmetic operation?

a)

addition

b)

multiplication

c)

subtraction

d)

square roots

136.

[LANGUAGE] A (a) is an explanation of why something is true.

137.

[BEGIN U4: Investigating Similarity] An object before transformation is called the _______.

a)

image

b)

pre-image

c)

post-image

d)

answer

138.

An object after transformation is called the _______.

a)

image

b)

pre-image

c)

post-image

d)

answer

139.

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

a)

(5,3)

b)

(20,12)

c)

(-20,-12)

d)

(-5,-3)

140.

Dilate point B by a scale factor of 1/2

a)

(1.5,-4)

b)

(-1.5,1)

c)

(-1,-1.5)

d)

(-2,-2)

141.

Dilate point B by a scale factor of 3:

a)

(12,0)

b)

(12,12)

c)

(4,3)

d)

(0,12)

142.

Which of the following are dilations?

a)

(x, y) → (x, 3y)

b)

(x, y) → (3x, 3y)

c)

(x, y) → (x, y - 3)

d)

(x, y) → (.5x, .4y)

143.

[END U4L1 (Dilations)] The point B (2, 1) was dilated to become point B' (6, 3). What was the scale factor?

a)

1/3

b)

2

c)

3

d)

1/2

144.

[BEGIN U4L3 (Similar Figures + Similarity Transformations)] A comparison of related quantities (like a:b or "a to b" or 1/2) is called a _______.

a)

mystery

b)

ratio

c)

pre-image

d)

IDK

145.

A proportion is an ___________ that compares two ratios.

a)

equation

b)

congruence statement

c)

proof

d)

definition

146.

We solve proportions by using the ____________.

a)

cross-product property

b)

property of equality ("whatever I do to one side of the equation, I must do to the other side of the equation")

c)

Pythagorean Theorem

d)

triangle congruence theorem

147.

Polygons that have congruent corresponding angles and proportional corresponding sides are _______.

a)

similar

b)

congruent

c)

the same

d)

equal

148.

Find side length X.

a)

16

b)

18

c)

2.4

d)

15

149.

Find side length X.

a)

30

b)

25

c)

15

d)

40

150.

The triangles are similar. Solve for the question mark.

a)

8

b)

12.5

c)

18

d)

24

151.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

152.

State if the triangles in each pair are similar. If so, state how you know they are similar.

a)

Yes, AA Similarity

b)

Yes, SSS Similarity

c)

Yes, SAS Similarity

d)

Not Similar

153.

If two figures are similar, the corresponding sides are ______________.

a)

equal

b)

congruent

c)

proportional

d)

none of these

154.

Determine whether the triangles are similar(name the postulate or theorem you used).

a)

SSS similar

b)

AA similar

c)

SAS similar

155.

Complete the similarity statement: △ACB ~ _______

a)

△HFG

b)

△HGF

c)

△FHG

d)

△FGH

156.

Are the triangles similar?

a)

Yes, by AA

b)

Not similar

c)

Yes, by SAS

d)

Yes, by SSS

157.

Are the triangles similar? If so, how?

a)

Similar by AA

b)

Similar by SAS

c)

Similar by SSS

d)

Not similar

158.

[END U3L3: Similar Figures + Similarity Theorems] Complete the similarity statement: △ADB ~ _______

a)

△ACE

b)

△AEC

c)

△EAC

d)

△ECA

159.

[BEGIN U4L4: Triangle Proportionality, Similarity Proofs] The TRIANGLE PROPORTIONALITY THEOREM says ___________ (check all that apply).

a)

All triangles have 3 angles.

b)

If a line segment divides two sides of a triangle proportionally, then it is parallel to the third side.

c)

If a line segment is parallel to one side of a triangle and intersects the other sides, then it divides those intersected sides proportionally.

d)

All triangles have 3 angles whose sum is 180 degrees.

160.

PROPORTIONAL PARTS AND PARALLEL LINES: If 3 or more parallel lines are intersected by two ________, then the parallel lines divide the ________ proportionally.

a)

perpendicular bisectors

b)

angles

c)

midpoints

d)

transversals

161.

Complete each proportion.
AB / BM = ? / CD

a)

BC

b)

AC

c)

MD

d)

MC

162.

Which proportion could be used to prove that $HJ\parallel KL$ ?

a)

$\frac{KL}{HJ}=\frac{KG}{LG}$

b)

$\frac{KH}{KG}=\frac{LG}{LJ}$

c)

$\frac{HK}{JL}=\frac{LG}{GK}$

d)

$\frac{GK}{HK}=\frac{GL}{LJ}$

163.

Find the missing length.

a)

14

b)

20

c)

16

d)

10

164.

Find x.

a)

54/7

b)

56/3

c)

11

d)

21/2

165.

Solve for X

a)

7.5

b)

4.8

c)

13.33

d)

5

166.

Select the proportion that shows the Triangle Proportionality Theorem.

a)

$\frac{6}{27}=\frac{7}{x}$

b)

$\frac{6}{21}=\frac{7}{x}$

c)

$\frac{7}{6}=\frac{x}{27}$

167.

What is the height of the flag pole?

Show your work.

a)

205

b)

105

c)

230

d)

135

168.

Find the height of the tree.

a)

8 ft

b)

12 ft

c)

13 ft

d)

15 ft

169.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

AA

b)

SSS

c)

SAS

d)

no similar

170.

Which similarity theorem, if any, proves that these triangles are similar?

a)

SSS

b)

SAS

c)

AA

d)

None, the triangles are not similar

171.

Which similarity theorem, if any, proves that these triangles are similar?

a)

SSS

b)

SAS

c)

AA

d)

None, the triangles are not similar

172.

Which similarity theorem, if any, proves that these triangles are similar?
(Hint: Look for non-labeled parts!)

a)

AA

b)

SAS

c)

SSS

d)

None, the triangles are not similar

173.

[END U4L4: Triangle Proportionality, Similarity Proofs] Give the reason for similarity.

a)

AA

b)

SAS

c)

SSS

d)

AAS

174.

[BEGIN U5TR U5L1 Intro to Trig Ratios & Missing Sides]

---

[LANGUAGE] What word was used a lot in this unit?

2 lines

175.

[LANGUAGE] What is another word was used a lot in this unit?

2 lines

176.

What side is opposite $\angle$ J?

a)

9

b)

40

c)

41

d)

none

177.

What side is the hypotenuse of the triangle?

a)

9

b)

40

c)

41

d)

none

178.

What is the sine ratio?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

179.

What is the cosine ratio?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

180.

What is the tangent ratio?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

181.

What is a common way to remember the definitions of the trig ratios?

a)

SAH COH TOA

b)

SOA COH TOA

c)

SOH CAH TOA

d)

ADJ OPP HYP

182.

What is $\cos A$ ?

a)

$\frac{29}{20}$

b)

$\frac{21}{29}$

c)

$\frac{20}{29}$

d)

$\frac{21}{20}$

183.

What is $\tan A$ ?

a)

$\frac{29}{20}$

b)

$\frac{21}{29}$

c)

$\frac{20}{29}$

d)

$\frac{21}{20}$

184.

What is $\tan\ C$ ?

a)

$\frac{20}{21}$

b)

$\frac{21}{29}$

c)

$\frac{20}{29}$

d)

$\frac{21}{20}$

185.

Which trig function does not include the hypotenuse?

a)

sine

b)

cosine

c)

tangent

186.

Find tan( $\alpha$ ) in the triangle.

a)

$\frac{21}{29}$

b)

$\frac{20}{29}$

c)

$\frac{21}{20}$

d)

$\frac{20}{21}$

187.

Find sin( $\alpha$ ) in the triangle.

a)

$\frac{12}{35}$

b)

$\frac{35}{37}$

c)

$\frac{35}{12}$

d)

$\frac{12}{37}$

188.

[END U5TR U5L1 Intro to Trig Ratios & Missing Sides]

Find tan(C).

a)

A

b)

B

c)

C

d)

D

189.

[BEGIN U5TR U5L2 Finding Missing Sides and Angles with Trig Ratios]

Find tan(X).

a)

32/40

b)

40/24

c)

32/24

d)

24/32

190.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

191.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

192.

What trigonometric ratio would be used to find the distance from the ship to the plane?

a)

sine

b)

cosine

c)

tangent

d)

inverse sine

193.

Find the missing side.

a)

36

b)

76.8

c)

12

d)

40

194.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

195.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

196.

What is the side opposite angle A?

a)

12

b)

13

c)

5

d)

25

197.

Solve for the missing angle ...

HINT 1: Which side lengths have values?

HINT 2: What trig ratio should be used?

HINT 3: How do we find the ANGLE?

a)

32°

b)

44°

c)

61°

d)

50°

198.

Solve for the missing angle ...

HINT 1: Which side lengths have values?

HINT 2: What trig ratio should be used?

HINT 3: How do we find the ANGLE?

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

199.

Solve for the missing angle ...

HINT 1: Which side lengths have values?

HINT 2: What trig ratio should be used?

HINT 3: How do we find the ANGLE?

a)

$9.4\degree$

b)

$55.2\degree$

c)

$20.15\degree$

d)

$19.4\degree$

200.

Choose the correct ratio.

a)

sin^-1(12/29)

b)

cos^-1(12/29)

c)

tan^-1(12/29)

d)

tan^-1(29/12)

201.

Solve for the missing angle ...

HINT 1: Which side lengths have values?

HINT 2: What trig ratio should be used?

HINT 3: How do we find the ANGLE?

a)

33°

b)

49°

c)

39°

d)

41°

202.

Solve for the missing angle ...

HINT 1: Which side lengths have values?

HINT 2: What trig ratio should be used?

HINT 3: How do we find the ANGLE?

a)

$50.2\degree$

b)

$93.1\degree$

c)

$12.6\degree$

d)

$42.2\degree$

203.

Choose the correct ratio.

a)

sin^-1(9/20)

b)

cos^-1(9/20)

c)

tan^-1(9/20)

d)

cos^-1(20/9)

204.

[BEGIN U5TR U5L3 Complementary Angles] Find the measure of the angle x.

a)

$95\degree$

b)

$85\degree$

c)

$35\degree$

d)

$45\degree$

205.

Solve for the missing angle ...

HINT 1: Which side lengths have values?

HINT 2: What trig ratio should be used?

HINT 3: How do we find the ANGLE?

a)

90^o

b)

10⁰

c)

130^o

d)

50^o

206.

Supplementary angle measures = (a) degrees.

207.

Complementary angle measures = (a) degrees.

208.

Find the complementary angle measures.

a)

75 and 105

b)

75 and 15

c)

25 and 65

d)

34 and 146

e)

38 and 52

209.

Find the missing angle.

a)

$72\degree$

b)

$68\degree$

c)

$90\degree$

d)

$78\degree$

210.

Sine is the ratio of the opposite leg / hypotenuse.

Cosine is the ratio of the adjacent leg / hypotenuse.

Tangent is the ratio of the opposite leg / adjacent leg.

In Right Triangle ABC with right angle A ...

If the cos C = 4 / 5, what is sin B?

a)

3 / 5

b)

3 / 4

c)

4 / 5

d)

5 / 4

211.

Sine is the ratio of the opposite leg / hypotenuse.

Cosine is the ratio of the adjacent leg / hypotenuse.

Tangent is the ratio of the opposite leg / adjacent leg.

In Right Triangle ABC with right angle A ...

If the sin C = 5 / 13, what is cos B?

a)

13 / 5

b)

5 / 13

c)

5 / 12

212.

Sine is the ratio of the opposite leg / hypotenuse.

Cosine is the ratio of the adjacent leg / hypotenuse.

Tangent is the ratio of the opposite leg / adjacent leg.

In Right Triangle ABC with right angle A ...

If the cos C = 8 / 10, what is sin B?

a)

10 / 8

b)

6 / 10

c)

8 / 10

213.

[END U5L3 Complementary Angles]

[END U5TR]

---

Sine is the ratio of the opposite leg / hypotenuse.

Cosine is the ratio of the adjacent leg / hypotenuse.

Tangent is the ratio of the opposite leg / adjacent leg.

In Right Triangle ABC with right angle A ...

If the sin C = 7 / 25, what is cos B?

a)

7 / 25

b)

7 / 24

c)

24 / 25

214.

[BEGIN U6AL10 Circles Test Review U6ATR][BEGIN U6AL1 (Circle Language)]

If you are given a radius, how can you find the diameter?

a)

Divide the radius by 2

b)

Square the radius

c)

Multiply the radius by 2

d)

Take the square root of the radius

215.

What part of the circle is present?

a)

Tangent

b)

Secant

c)

Chord

d)

Diameter

216.

What part of the circle is present?

a)

diameter

b)

radius

c)

chord

d)

secant

217.

What part of the circle is present?

a)

Minor Arc

b)

Major Arc

c)

Semi-Circle

d)

Central Angle

218.

What part of the circle is present?

a)

Minor Arc

b)

Major Arc

c)

Semi-Circle

d)

Central Angle

219.

What part of the circle is present?

a)

Major Arc

b)

Minor Arc

c)

Central Angle

d)

Inscribed Angle

220.

What part of the circle is present?

a)

Major Arc

b)

Minor Arc

c)

Central Angle

d)

Inscribed Angle

221.

A segment that goes through a circle intersecting the circle at two points.

a)

diameter

b)

chord

c)

tangent

d)

secant

222.

A segment/chord that runs through the center of the circle (the longest chord).

a)

Chord

b)

Diameter

c)

Radius

d)

Inscribed Angle

223.

[END U6AL1 (Circle Language)] The distance from the center of a circle to the boundary of a circle (half of the diameter).

a)

Chord

b)

Diameter

c)

Radius

d)

Inscribed Angle

224.

[BEGIN U6AL2 (Central and Inscribed Angles)] Angle a is a(n) ___ angle.

a)

central

b)

inscribed

225.

Angle b is a(n) ___ angle.

a)

central

b)

inscribed

226.

Find the measure of the marked angle.

a)

52

b)

104

c)

26

d)

13

227.

Find the measure of the marked arc.

a)

15

b)

30

c)

60

d)

7.5

228.

Find the measure of the marked angle.

a)

22

b)

44

c)

11

d)

66

229.

Find the measure of the marked angle.

a)

140

b)

70

c)

35

d)

210

230.

Find m∠PRQ.

a)

39°

b)

90°

c)

51°

d)

15°

231.

Solve for x.

a)

5

b)

20

c)

40

d)

85

232.

Find the measure of arc NM

a)

192^o

b)

217^o

c)

186^o

d)

124^o

233.

Find the value of x.

(a)

234.

[END U6AL2 (Central and Inscribed Angles)] In a circle (or congruent circles), the measure of an arc is:

a)

equal to twice the measure of its corresponding inscribed angle

b)

equal to the measure of its corresponding inscribed angle

c)

equal to half of the measure of its corresponding inscribed angle

d)

equal to four cups of wheat flour

235.

[BEGIN U6AL3L4 (Angles Inside and Outside Circle)] Find the measure of angle ABD.

a)

14

b)

51

c)

37

d)

65

236.

Solve for x.

a)

29

b)

33

c)

41.5

d)

50

237.

What is the measure of angle HKI?

a)

72

b)

73

c)

74

d)

75

238.

Find the m∠MNQ.

a)

89⁰

b)

45⁰

c)

158⁰

d)

22⁰

239.

Find the arc indicated.

a)

55

b)

175

c)

115

d)

285

240.

Find the arc indicated.

a)

112

b)

143

c)

53

d)

127

241.

Find the arc indicated.

a)

78

b)

51

c)

-78

d)

102

242.

Find the angle indicated.

a)

70

b)

50

c)

60

d)

55

243.

[END U6AL3L4 (Angles Inside and Outside Circle)] Find the arc indicated.

a)

185

b)

75

c)

110

d)

100

244.

[BEGIN U6AL6 (Triangles and Quadrilaterals Inscribed in Circles + Tangents)] AB is a diameter. The measure of angle B is 58 degrees. Find the m < A.

a)

32

b)

128

c)

90

d)

There is not enough information to determine $m\angle A$

245.

AB is a diameter. The measure of angle C is 90 degrees and angle A is 79 degrees. Find the m < B.

a)

101

b)

90

c)

11

246.

AB is a diameter. The measure of angle C is 90 degrees and angle B is 68 degrees. Find the m < A.

a)

90

b)

112

c)

22

247.

AB is a diameter. The measure of angle C is 90 degrees and angle A is 17 degrees. Find the m < B.

a)

73

b)

163

c)

90

248.

The m < B = 123 degrees. Find the m < D.

a)

180

b)

90

c)

57

249.

The m < C = 27 degrees. Find the m < A.

a)

180

b)

153

c)

127

250.

Find the m < x.

a)

112 degrees

b)

98 degrees

c)

132 degrees

251.

Find the m < y.

a)

112 degrees

b)

82 degrees

c)

144 degrees

252.

In the inscribed quadrilateral ABCQ, opposite angles are

a)

congruent

b)

supplementary

c)

complementary

d)

sum to 360^o

253.

\angle X=

a)

$96\degree$

b)

$129$

c)

$84\degree$

d)

$49\degree$

254.

A tangent line intersecting with a radius always creates a ____________ angle

a)

right

b)

acute

c)

obtuse

d)

straight

255.

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?" (the length of the hypotenuse)

a)

15

b)

6

c)

-24

d)

14

256.

Find the radius r

a)

2

b)

3

c)

4

d)

5

257.

Determine if a tangent line is shown in the picture.

a)

Yes

b)

No

c)

Not sure

258.

Assume that the lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x to the nearest tenth.

a)

11.7

b)

10.8

c)

13.0

d)

14.2

259.

[END U6AL6 (Triangles and Quadrilaterals Inscribed in Circles + Tangents)] Find x. Assume that segments that appear to be tangent are tangent.

a)

11.2

b)

18.0

c)

25.0

d)

30.0

260.

[BEGIN U6AL8 (Arc Length and Sector Area)] Find the arc length of arc AB.

a)

12.57 units

b)

75.40 units

c)

24 units

d)

125.66 units

261.

Find the arc length of arc AB.

a)

1.5 units

b)

18.85 units

c)

4.71 units

d)

200 units

262.

Find the area of the shaded space.

a)

113.10 units squared

b)

150.80 units squared

c)

157.82 units squared

d)

10.92 units squared

263.

Find the area of the sector.

a)

A

b)

B

c)

C

d)

D

264.

Find the area of the shaded sector.

a)

9.23 in²

b)

10.51 in²

c)

31.42 in²

d)

38.27 in²

265.

If Pacman's mouth, when open, is 70° and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body?

a)

161.97 mm²

b)

What's Pacman?

c)

39.1 mm²

d)

9.77 mm²

266.

[BEGIN U6AL9 (Equation of Circle)] In the equation (x - 3)²+ (y - 2)²= 16, the center of the circle is...

a)

(3, 2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

267.

In the equation (x - 4)²+ (y - 3)²= 25, the radius is

a)

4

b)

3

c)

5

d)

25

268.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

269.

See Picture

a)

A

b)

B

c)

C

d)

D

270.

What is the equation of the circle?

a)

(x + 1)² + (y + 1)² = 3

b)

(x + 1)² + (y - 1)² = 3

c)

(x + 1)² + (y + 1)² = 9

d)

(x - 1)² + (y - 1)² = 9

271.

What is the equation for this circle?

a)

(x+1)+(y+1)=9

b)

x²+y²=9

c)

x+y=9

272.

a)

A

b)

B

c)

C

d)

D

273.

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

a)

(x - 5)²+ (y + 2)²= 144

b)

(x - 5)² + (y + 2)² = 36

c)

(x + 5)²+ (y - 2)²= 36

d)

(x + 5)²+ (y - 2)²= 144

274.

[END U6AL10 Circles Test Review U6ATR]
[END U6AL9 (Equation of Circle)]

What is the center of the circle with this equation is (x+2)²+(y-4)²=41?

a)

(2,-5)

b)

(-2,4)

c)

(2,-4)

d)

(-2, -4)

275.

[U6B Unit Circle ... 001-020 Special Right Triangles ... 021-040 Right Triangles on the Coordinate Plane ... 041-060 What is a Radian? Converting between Radians and Degrees | 061-080 Determining Values of Sine, Cosine, and Tangent ... 081-120 U6B Unit Circle Test Review U6BTR ...]

[BEGIN U6B Unit Circle Test Review U6BTR]
[BEGIN U6BL1 Special Right Triangles]

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I ...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

276.

In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?

a)

It is the same length as the given leg.

b)

Multiply that leg's length by √2.

c)

Multiply that leg's length by 2.

d)

Divide that leg's length by √2.

277.

I have been given a hypotenuse in this 45-45-90 triangle. How do I find the length of a leg of the triangle?

a)

Multiply by √2

b)

Divide by √2

c)

It's the same length as the hypotenuse.

d)

Divide by 2

278.

What type of special right triangle is this?

a)

45-45-90

b)

30-60-90

c)

not a special right triangle

279.

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

280.

I have been given the hypotenuse in this 30-60-90 triangle. How do I find the short leg?

a)

Multiply 6 by 2

b)

Multiply 6 by √3

c)

Divide 6 by 2

d)

Divide 6 by √3

281.

I have been given the long leg in this 30-60-90 triangle. How do I find the hypotenuse?

a)

Divide 8 by √3

b)

Divide 8 by 2

c)

Divide 8 by 2, then multiply that answer by √2

d)

Divide 8 by √3, then multiply that answer by 2

282.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

283.

What is the length of y in this 45-45-90 triangle?

a)

45

b)

5√2

c)

90

d)

5

284.

[END U6BL1 Special Right Triangles]

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

285.

[BEGIN U6BL2L3 Right Triangles In The Coordinate Plane]

A "unicycle" has one wheel ... a "unicorn" has one horn ... in the card game "Uno", I must say "Uno!" when I have one card left ... a "unit" circle has a radius of _____.

4 lines

286.

What is the radius of this UNIT circle?

a)

$\sqrt[]{2}$

b)

1

c)

$\sqrt[]{3}$

d)

2

287.

What is the ratio of the ADJACENT side to the HYPOTENUSE
(AKA $\cos\ \theta$ )?

a)

$\frac{1}{b}$

b)

$\frac{b}{1}=1$

c)

$\frac{a}{1}=a$

d)

$\frac{1}{a}$

288.

What is the ratio of the OPPOSITE side to the HYPOTENUSE
(AKA $\sin\ \theta$ )?

a)

$\frac{a}{b}$

b)

$\frac{b}{1}=1$

c)

$\frac{a}{1}=a$

d)

$\frac{b}{a}$

289.

What is the ratio of the OPPOSITE side to the ADJACENT side
(AKA $\tan\ \theta$ )?

a)

$\frac{a}{b}$

b)

$\frac{b}{1}=1$

c)

$\frac{a}{1}=a$

d)

$\frac{b}{a}$

290.

The UNIT CIRCLE has a radius of ______; its center is at the _______.

The UNIT CIRCLE is important because it provides a ______ way to understand and calculate trigonometric functions like sine, cosine, and tangent for any angle.

a)

diameter; radius; EASY

b)

$\sqrt[]{3}$ ; y = x; DIFFICULT

c)

$\sqrt[]{2}$ ; equator; HEARTFELT

d)

1; origin; VISUAL

291.

What is tan 45°?

a)

1

b)

^√2/₂

c)

^√3/₂

d)

½

292.

What is sin 45°?

a)

1

b)

^√3/₂

c)

½

d)

^√2/₂

293.

What is sin 30°?

a)

^√3/₂

b)

1

c)

½

d)

^√2/₂

294.

[END U6BL2L3 Right Triangles In The Coordinate Plane]

What is sin 90°?

a)

1

b)

0

c)

undefined

d)

½

295.

[BEGIN U6BL4 What Is A Radian? AND U6BL5 AND Converting between Radians and Degrees]

A RADIAN is the measure of a central angle that intercepts an arc whose length is equal to the ________.

a)

diameter

b)

radius

296.

RADIANS and DEGREES give us two different ways to measure ________.

a)

angles

b)

arc length

c)

sector area

d)

circumference

297.

To convert from DEGREES to RADIANS ... ________.

a)

multiply by

$\frac{π}{180°}$

b)

multiply by
$\frac{180°}{π}$

c)

multiply by
$\frac{π}{\sqrt{2}}$

d)

multiply by
$\frac{π}{\sqrt{3}}$

298.

To convert from RADIANS to DEGREES ... ________.

a)

multiply by

$\frac{π}{180°}$

b)

multiply by
$\frac{180°}{π}$

c)

multiply by
$\frac{π}{\sqrt{2}}$

d)

multiply by
$\frac{π}{\sqrt{3}}$

299.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

300.

Convert $\frac{π}{4}$ from radians to degrees.

a)

90⁰

b)

45⁰

c)

60⁰

d)

30⁰

301.

Convert 100⁰ to radians.

a)

$\frac{5π}{9}$

b)

$\frac{9π}{5}$

c)

$\frac{5π}{8}$

d)

$\frac{10π}{9}$

e)

$\frac{9π}{10}$

302.

What is the degree measure of an angle with a radian measure of $\frac{7}{4}\pi$ ?

a)

$310\degree$

b)

$320\degree$

c)

$315\degree$

d)

$330\degree$

303.

Convert to degrees: 11π/6

a)

300°

b)

315°

c)

330°

d)

350°

304.

[END U6BL4 What Is A Radian? AND U6BL5 AND Converting between Radians and Degrees]

Convert 150⁰ to radians.

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

305.

[BEGIN U6BL5 Determining Values of Sine, Cosine, and Tangent]

tan(7π/4)

a)

-1

b)

1

c)

√2/2

d)

undefined

306.

sin(7π/6)

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

307.

tan (π)

a)

undefined

b)

0

c)

1

d)

-1

308.

What are the coordinates of 3π/4 radians on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

309.

What is $\cos\left(\frac{5\pi}{6}\right)$ ?

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{3}}{2}$

d)

$-\frac{\sqrt{3}}{2}$

310.

What are the coordinates of $\frac{4\pi}{3}$ radians?

a)

$\left(-\frac{1}{2},-\frac{\sqrt{3}}{2}\right)$

b)

$\left(\frac{1}{3},\frac{\sqrt{3}}{3}\right)$

c)

$\left(\frac{\sqrt{3}}{2},\frac{\sqrt{2}}{2}\right)$

d)

$\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)$

311.

What is the order of the coordinate pairs for the points on the unit circle?

a)

$\left(\tan\theta,\sin\theta\right)$

b)

$\left(\cot\theta,\cos\theta\right)$

c)

$\left(\sin\theta,\cos\theta\right)$

d)

$\left(\cos\theta,\sin\theta\right)$

312.

What are the coordinates of $225\degree$ on the unit circle?

a)

$\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

b)

$\left(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

c)

$\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$

d)

$\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$

313.

sin(7π/6)

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

314.

[END U6BL5 Determining Values of Sine, Cosine, and Tangent]

[END U6B Unit Circle Test Review U6BTR]

tan(-π)

a)

undefined

b)

0

c)

1

d)

-1

315.

[BEGIN U7 Volume Test Review U7TR ]

[BEGIN Volume of Prisms and Cylinders]

Find the volume of the triangular prism.

V = (base area)(height)

a)

960 cm³

b)

240 cm³

c)

1920 cm³

d)

400 cm³

316.

Find the volume of the rectangular prism.

a)

55 yd³

b)

121 yd³

c)

22 yd³

d)

330 yd³

317.

Find the volume (leave answers in terms of 'pi') ...

a)

484π cm3

b)

88π cm3

c)

176π cm³

d)

1937π cm³

318.

Calculate the volume:

a)

1120 ft ³

b)

600 ft ³

c)

560 ft ³

d)

64 ft ³

319.

Find the volume of this triangular prism.

a)

1440 cm³

b)

60 cm³

c)

720 cm³

d)

180 cm³

320.

[END Volume of Prisms and Cylinders]

What is the volume of the cylinder?

a)

4523.9 in³

b)

18095.6 in³

c)

942.5 in³

d)

120 in³

321.

[BEGIN Volume of Pyramids, Cones, and Spheres]

What shape is this?

a)

Cone

b)

Sphere

c)

Cube

d)

Pyramid

322.

Find the volume ...

a)

2,144.66 m³

b)

1,608.49 m³

c)

536.17 m³

d)

498.62 m³

323.

Find the volume.

a)

144 cm³

b)

288 cm³

c)

48 cm³

d)

24 cm³

324.

Find the volume. The radius is 10 units.

a)

4,188.8

b)

1,333.3

c)

2,364.3

d)

5,000.3

325.

Find the volume.

a)

452.16cm³

b)

452cm

c)

1808.64cm³

d)

1808.65cm³

326.

Find the volume.

a)

$4\pi$ ft³

b)

$12\pi$ ft³

c)

$48\pi$ ft³

d)

$16\pi$ ft³

327.

[END Volume of Pyramids, Cones, and Spheres]

Find the volume of the hemisphere (HINT: this is half of a sphere) ...

a)

$288\pi$ cm³

b)

$72\pi$ cm³

c)

$36\pi$ cm³

d)

$144\pi$ cm³

328.

[BEGIN Volume of Composite Solids]

What shape(s) make each layer of the cake?

a)

Cone

b)

Cylinder

c)

Pyramid

d)

Rectangular Prism

329.

What is the volume of the composite solid?

a)

19 in³

b)

24 in³

c)

29 in³

d)

34 in³

330.

Find the volume of the following shape.

a)

4155.27 m³

b)

1038.82 m³

c)

804.24 m³

d)

1005.31 m³

331.

What is the volume of the composite solid?

a)

301.6 cm³

b)

502.7 cm³

c)

268.1 cm³

d)

167.6 cm³

332.

Find the volume ...

a)

1412.4 cm³

b)

965.2 cm³

c)

1123.6 cm³

d)

1348.6 cm³

333.

Which equation would you use to find the volume of this composite figure?

a)

8³ + ⁴/₃π(8)³

b)

8³ + ⁴/₃π(4)³

c)

8³ + (¹/₂)(⁴/₃)π(4)³

d)

8² + ⁴/₃π(8)³

e)

8²+(¹/₂)8²π

334.

[END Volume of Composite Solids]

Find the volume of the composite figure.

a)

2400 ft³

b)

1920 ft³

c)

4128 ft³

d)

2112 ft³

335.

[BEGIN Density]

What is the formula for density?

a)

density = mass x volume

b)

density = mass / volume

c)

density = mass + volume

d)

density = mass - volume

336.

Frank has a paper clip. It has a mass of 9g and a volume of 3cm³. What is its density?

a)

3 g/cm³

b)

1/3 g/cm³

c)

27 g/cm³

d)

39 g/cm³

337.

Which definition best matches the term population density?

a)

human beings in general

b)

number of people in a particular area

c)

A measurement of people for a specific area

d)

All the inhabitants of a particular area

338.

Which state has the greatest population density?

a)

New Jersey

b)

Rhode Island

c)

Connecticut

d)

Vermont

339.

[END Density]

[END U7 Unit Test Review U7TR]

Which state has the population density of 41 people per square mile?

a)

Connecticut

b)

Maryland

c)

Maine

d)

New York

340.

[BEGIN U8 Probability Test Review U8TR]

[BEGIN Probability Notations and Organizing Data (Set Notation and Venn Diagrams)]

What does this symbol ( ∩ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

341.

Identify the shaded area...

a)

A∩B

b)

A∪B

c)

A'∩B'

d)

A'∪B'

342.

List the elements of the the set: B'

a)

{ 1 , 5 , 6 }

b)

{ 1 , 2 , 3 , 5 , 6 , 9 }

c)

{ 2 , 3 , 9 }

d)

None of these

343.

How many senior boys play football and wrestle?

a)

9

b)

12

c)

18

d)

39

344.

[END Probability Notations and Organizing Data (Set Notation and Venn Diagrams)]

How many senior boys play football but do not wrestle?

a)

9

b)

12

c)

18

d)

104

345.

[BEGIN Addition Rule]

What is the formula for the addition rule of probability?

a)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

b)

P(A ∩ B) = P(A) - P(B)

c)

P(A ∪ B) = P(A) * P(B)

d)

P(A ∩ B) = P(A) + P(B)

346.

Find the probability of choosing a card at random that is a spade OR a 7

a)

1/52

b)

1/13

c)

4/13

d)

17/52

347.

A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a king or a club?

a)

1/52

b)

16/52

c)

17/52

d)

None of the above

348.

A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability that it is yellow or green?

a)

3/10

b)

4/10

c)

7/10

d)

None of the above

349.

[END Addition Rule]

A number from 1 to 10 is chosen at random. What is the probability of choosing a 4 or an odd number?

a)

3/5

b)

1/2

c)

1/5

d)

None of the above

350.

[BEGIN Multiplication Rule]

What is the significance of calculating probabilities in real-life scenarios?

a)

It helps in making informed decisions based on the likelihood of various outcomes.

b)

It guarantees success in all endeavors.

c)

It eliminates uncertainty in decision-making.

d)

It is only useful in academic settings.

351.

What does 'without replacement' mean in probability?

a)

It means that items are returned to the pool after selection.

b)

It means that once an item is selected, it is not returned to the pool for subsequent selections.

c)

It refers to selecting items in a random order without any restrictions.

d)

It indicates that all items must be selected at once.

352.

Jim picks a diamond out of a deck of cards, replaces it and gets a diamond again. What is the probability this happened. (There are 13 diamonds, and 52 cards in a deck)

a)

1/16

b)

2/13

c)

4/17

d)

1/21

353.

What is the probability that the person picked will be a boy given they speak german?

a)

.7273

b)

.4

c)

.16

d)

.22

354.

[END Multiplication Rule]

The spinner below is divided into 4 equal parts. It is spun once, and the coin is flipped once. What is the probability of obtaining red on the spinner followed by heads on the coin?

a)

$\frac{1}{8}$

b)

$\frac{1}{4}$

c)

$\frac{3}{4}$

d)

$\frac{7}{8}$

355.

[BEGIN Conditional Probability]

P(A∣B)=

a)

P(A⋂B)/P(A)

b)

P(A⋂B)/P(B)

c)

P(A⋃B)/P(A)

d)

P(A⋃B)/P(B)

356.

What is the probability that a student has a brother given that they do not have a sister?

*Write your answer as a fraction*

(a)

357.

P(Sandals|Pants):

a)

4/20

b)

6/15

c)

1/2

d)

2/7

358.

What is the probability that a student plays sports given that they do community service?

a)

$\frac{5}{15}$

b)

$\frac{5}{9}$

c)

$\frac{5}{27}$

d)

$\frac{9}{15}$

359.

[END] Conditional Probability]

A box contains 3 blue marbles, 5 red marbles, and 4 white marbles.

Find P(red given not white).

a)

3/8

b)

1/4

c)

5/12

d)

5/8

360.

[BEGIN Permutations and Combinations]

A DJ has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

Is this a Permutation or Combination?

a)

Permutation - the order of the songs matters

b)

Combination - the order of the songs does not matter

361.

The ski club has 10 members and is choosing three officers for the season. How many ways can they pick a captain, co-captain and secretary?

a)

720

b)

120

c)

10!

d)

3!

362.

You have DVD collection with 20 DVDs. You can only take five DVDs with you on vacation. How many different sets of five DVDs can you take?

a)

15504

b)

20!

c)

5!

d)

$\frac{5}{20}=0.25$

363.

A group of 25 people are going to run a race. The top 8 finishers advance to finals. How many different combinations can there be?

a)

625

b)

4.36 X 10¹⁰

c)

1,081,575

364.

[END Permutations and Combinations]

Ambry must submit 4 paintings as part of her application to art school. If she has 25 to choose from, how many ways can she pick 4?

a)

12,650

b)

303,600

c)

100

d)

254

365.

[BEGIN Probability Distributions and Expected Value]

A fair, 6-sided dice is thrown 18 times.

Roughly how many times would you expect the number 6 to come up?

a)

1

b)

3

c)

6

366.

Is this a probability distribution?

a)

No

b)

Yes

367.

Given the probability model in the table below, what is the expected value of the random variable?
X 50 20 5
P(X) 0.1 0.3 0.6

a)

14

b)

4.67

c)

5

d)

7.5

368.

A student group sells 500 raffle tickets for $2 each. At the drawing the top prize will be a gift certificate for $100. Second prize will be a $50 gift card and there will be five 3rd prizes, each a $20 gift card. Do you expect to win or lose (on average)? How much?

a)

lose an average of $5.50

b)

lose an average of $1.50

c)

win an average of $2.00

d)

lose an average of $10.00

369.

[END U8 Probability Test Review U8TR]

[END Probability Distributions and Expected Value]

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?

a)

$12.50

b)

$5

c)

$7.50

d)

$10

GPPPU1-8 SY2026 (Poly, Proofs, Cong, Sim, RightTri, Vol, Prob)

Total questions: 369

Worksheet time: 119hrs 48mins